Question

Convert the following to the equivalent indicated. 2 in \(=\) _______ \(\mathrm{mm}\)

Short answer

2 inches is equal to 50.8 millimeters.

Step-by-step solution

Identify Conversion Factor

To convert inches to millimeters, we need to find the conversion factor. The standard conversion is 1 inch = 25.4 millimeters.

Apply Conversion Factor

Multiply the given inches by the conversion factor to convert to millimeters. So, for 2 inches: \[ 2 ext{ inches} imes 25.4 rac{ ext{millimeters}}{ ext{inch}} = 50.8 ext{ millimeters} \]

Calculate

Perform the multiplication to find the result: \[ 2 imes 25.4 = 50.8 \]Thus, 2 inches is equal to 50.8 millimeters.

Key concepts

Conversion Factor

A conversion factor is a numerical value used to change units from one measurement system to another. It's crucial when you need to convert between different systems, such as imperial to metric. Conversion factors are derived from equivalences between units.
- For example, 1 inch is equivalent to 25.4 millimeters.
- This number, 25.4, is the conversion factor for changing inches into millimeters.
When applying a conversion factor, you multiply your original measurement by this number. This allows you to effectively "transpose" values from one unit into another. It's important to use the correct conversion factor for accurate results, so double-check your units!

Inches to Millimeters

Converting inches to millimeters involves using a specific conversion factor derived from the relationship between these two units. Inches are part of the imperial system, while millimeters are part of the metric system.
- 1 inch is precisely 25.4 millimeters. This is a fixed ratio used for converting measurements between these units.
- To convert inches to millimeters, you multiply the number of inches by 25.4. For instance, to convert 2 inches to millimeters, simply calculate: \(2 \times 25.4 = 50.8\). This means that 2 inches equals 50.8 millimeters. This computation ensures that you accurately change the unit from an imperial length to a metric one.

Mathematical Calculations

Mathematical calculations in unit conversions typically involve multiplication. Here's how you handle them for converting units like inches to millimeters:
- Identify the conversion factor between the units. For inches to millimeters, it's 25.4.
- Take the measurement you wish to convert (e.g., 2 inches) and multiply it by the conversion factor. For example, start with 2 inches:
\[ 2 \times 25.4 = 50.8 \]\These calculations show how multiplying your original value by the conversion factor translates it into the desired unit. Remember, the accuracy of your result hinges on correctly applying the conversion factor. Consistent practice with these calculations will build confidence in converting any unit efficiently.